In what precedes we have determined the position of
If
Thus the polar equation of a straight line is of the form
- Polar coordinates are sometimes defined so that
may be positive or negative. In this case two pairs of coordinates— and —correspond to the same point. The distinction between the two systems may be illustrated by means of the equation , where , . According to our definitions must be positive and therefore : the equation represents one branch only of a hyperbola, the other having the equation . With the system of coordinates which admits negative values of , the equation represents the whole hyperbola.↩︎
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